1
Module 6, Chapter 5: Accounting and the Time Value of Money
5.1 Basic Time Value Concepts
Q. What does the time value concept of money state?
- It states that a dollar is worth more today than it will be worth in the future.
Q. Why is the time value concept of money important?
- When deciding among investment proposals, it's essential to be able to compare today's dollar and
tomorrow's dollar.
Q. What is the present value concept?
- Present value is the current worth of a future cash flow given a specified rate of return.
- "How much is the money that I'll receive in the future worth to me today?"
Q. Which 8 areas of accounting use present value-based measurements?
1) Notes
2) Leases
3) Pensions and other retirement benefits
4) Long-term assets
5) Stock-based compensation
6) Business combinations
7) Disclosures
8) Environmental liabilities
Present value-based accounting Explanation
measure
Notes For long-term receivables or payables that don't have interest
rates matching current market rates, companies adjust their value
to reflect what they're truly worth today.
Leases For long-term leases, companies calculate what those future lease
payments are worth today and record both an asset (right to use
property) and a liability (obligation to pay) on their balance sheet.
Pensions and other retirement benefits This involves estimating the cost today of the benefits companies
promise to pay employees after they retire.
Long-term assets This means deciding what long-term investments (like buildings
or equipment) are worth today, especially when payments are
spread out over time, or if those assets lose value (impairment).
Stock-based compensation This is about determining the present value of the stock/stock
options companies give to employees as part of their pay.
Business combinations When companies merge or one company buys another, this is
about measuring the value of what’s being acquired — such as
, 2
debts, contracts, and assets — in today’s terms.
Disclosures This refers to calculating the present value of future income from
resources like oil and gas, and sharing that information in
financial reports.
Environmental liabilities This is estimating today’s cost of cleaning up or restoring the
environment in the future when assets are retired (like closing a
mine or a factory).
Q. What is the formula for simple interest?
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑝 × 𝑖 × 𝑛
p = principal (the amount borrowed or invested)
i = rate of interest for a single period
n = number of periods (years, or portions of a year, that the principal is outstanding)
On March 1, Ace Corporation borrowed $10,000 from a bank by signing a 4-month note with a 6% annual
simple interest rate.
How much interest will Ace Corporation owe at maturity?
- Interest = 10,000 x 6% x (4/12) = 200
What is the total amount Ace Corporation must repay at the end of the note?
- Principal plus interest = 10,000 + 200 = 10,200
Q. What is compound interest?
- Compound interest is when interest is calculated both on the initial principal but also on accumulated
interest that has not been paid or withdrawn.
Q. What does the term “periods” mean, as it relates to compound interest?
- "Periods" refers to the specific intervals at which interest is calculated and added to the principal
balance.
Q. What is the formula for Number of Periods?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑒𝑟𝑖𝑜𝑑𝑠 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑌𝑒𝑎𝑟𝑠 × 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑𝑠/𝑌𝑒𝑎𝑟
Q. When interest is compounded more than once a year, e.g. semiannually/quarterly/monthly, why is the
interest rate divided?
- The interest rate is divided because you're breaking the year into smaller periods — and to apply
interest correctly each time, you need to use a smaller rate that corresponds to each period.
Q. What is the formula for Compounding Period Interest Rate?
𝐴𝑛𝑛𝑢𝑎𝑙 𝑅𝑎𝑡𝑒
𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑𝑠/𝑌𝑒𝑎𝑟
Example: If you have 6% compounded annually for 5 years, then i = 6% and n = 5. If you have 6% compounded
semiannually for 5 years, then i = 3% and n = 10.
, 3
Q. What is the formula for future value of a single sum?
𝐹𝑉 = 𝑃𝑉(𝐹𝑉𝐹𝑛,𝑖 )
FV = Future value
PV = Present value
FVFn,i = Future value factor for n periods at i interest
Q. What is the formula for future value factor?
𝑛
𝐹𝑉𝐹𝑛,𝑖 = (1 + 𝑖)
FVFn,i = Future value factor for n periods at i interest
i = rate of interest for a single period
n = number of periods
𝑛
Another variation of the future value formula: 𝐹𝑉 = 𝑃𝑉(1 + 𝑖)
Put it into Practice, LO 5.1 Compute Simple and Compound Interest
Katie Boylen invests $20,000 at 6% annual interest, leaving the money invested without withdrawing any of
the interest for 6 years. At the end of the 6 years, Katie withdraws the accumulated amount of money.
a) Compute the amount Katie would withdraw assuming the investment earns simple interest.
Interest = $20,000 * 0.06 * 6 = $7,200
Amount withdrawn = $20,000 + $7,200 = $27,200
b) Compute the amount Katie would withdraw assuming the investment earns interest compounded
annually.
Here, n = 6
FV = $20,000(1 + 0.06)6 = $28,370
c) Compute the amount Katie would withdraw assuming the investment earns interest compounded
semiannually.
Here, n = 6 x 2 and i = 6 ÷ 2 = 3
FV = $20,000(1 + 0.03)12 = $28,515
5.2 Single-Sum Problems
Q. What are the 2 categories of single-sum problems?
1) Computing the unknown future value of a known single sum of money that is invested now for a
certain number of periods at a certain interest rate.
2) Computing the unknown present value of a known single sum of money in the future that is
discounted for a certain number of periods at a certain interest rate.
Q. What is the formula for the present value of a single sum?
1
𝑃𝑉 = 𝐹𝑉(𝑃𝑉𝐹𝑛,𝑖 ) 𝑜𝑟 𝑃𝑉 = 𝐹𝑉( 𝑛 )
(1+𝑖)
PV = Present value (principal or sum)
FV = Future value
PVFn,i = Present value factor for n periods at i interest
, 4
Q. What is the formula for the present value factor?
1
𝑃𝑉𝐹𝑛,𝑖 = 𝑛
(1+𝑖)
Put it into Practice, LO 5.2 Compute Future and Present Values of 1
Using the appropriate interest table, answer the question in each scenario. (Each case is independent of the
others.)
a. What is the future value of $7,000 at the end of 5 years at 8% interest compounded annually?
According to the interest table, the future value factor for n = 5, i = 8%:
FV = 7,000 * 1.46933 = $10,285
b. What is the present value of $7,000 due 8 periods from now, discounted at 6%?
According to the interest table, the present value factor for n = 8, i = 6%:
PV = 7,000 * 0.62741 = $4,392
c. Vince needs to accumulate $1,000,000 for future expansion plans. The company’s money market fund
has a balance of $92,296 and has a guaranteed interest rate of 10%. How many years (with annual
compounding) must Vince leave that balance in the fund to get his desired $1,000,000?
FV = 1,000,000 and PV = 92,296
We need to find the future value factor, knowing that i = 10%
1,000,000 ÷ 92,296 = 10.83470
10.83471 corresponds to n = 25 years
d. Assume that Vince desires to accumulate $1 million in 15 years using the money market fund balance of
$182,696. At what interest rate must Vince’s investment compound annually?
FV = 1,000,000 and PV = 182,696
We need to find the future value factor, knowing that n = 15
1,000,000 ÷ 182,696 = 5.47357
5.47357 corresponds to i = 12%
5.3 Future Value Annuities
Q. What are annuities?
- Annuities are a series of equal payments or receipts that occur at regular intervals over a specified
period.
Q. What are examples of annuities?
- Liabilities: bond interest payments, lease payments, regular pension contributions
- Assets: regular receipt of loan repayments from customers, rental income from owned properties
Q. What are the 3 requirements of annuities?
1) Periodic payments or receipts (called rents) of the same amount
2) Same-length interval between such rents
3) Compounding of interest once each interval
Q. What are the 2 types of annuities?
1) Ordinary Annuity: Rents occur at the end of each period.
2) Annuity Due: Rents occur at the beginning of each period.
Module 6, Chapter 5: Accounting and the Time Value of Money
5.1 Basic Time Value Concepts
Q. What does the time value concept of money state?
- It states that a dollar is worth more today than it will be worth in the future.
Q. Why is the time value concept of money important?
- When deciding among investment proposals, it's essential to be able to compare today's dollar and
tomorrow's dollar.
Q. What is the present value concept?
- Present value is the current worth of a future cash flow given a specified rate of return.
- "How much is the money that I'll receive in the future worth to me today?"
Q. Which 8 areas of accounting use present value-based measurements?
1) Notes
2) Leases
3) Pensions and other retirement benefits
4) Long-term assets
5) Stock-based compensation
6) Business combinations
7) Disclosures
8) Environmental liabilities
Present value-based accounting Explanation
measure
Notes For long-term receivables or payables that don't have interest
rates matching current market rates, companies adjust their value
to reflect what they're truly worth today.
Leases For long-term leases, companies calculate what those future lease
payments are worth today and record both an asset (right to use
property) and a liability (obligation to pay) on their balance sheet.
Pensions and other retirement benefits This involves estimating the cost today of the benefits companies
promise to pay employees after they retire.
Long-term assets This means deciding what long-term investments (like buildings
or equipment) are worth today, especially when payments are
spread out over time, or if those assets lose value (impairment).
Stock-based compensation This is about determining the present value of the stock/stock
options companies give to employees as part of their pay.
Business combinations When companies merge or one company buys another, this is
about measuring the value of what’s being acquired — such as
, 2
debts, contracts, and assets — in today’s terms.
Disclosures This refers to calculating the present value of future income from
resources like oil and gas, and sharing that information in
financial reports.
Environmental liabilities This is estimating today’s cost of cleaning up or restoring the
environment in the future when assets are retired (like closing a
mine or a factory).
Q. What is the formula for simple interest?
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = 𝑝 × 𝑖 × 𝑛
p = principal (the amount borrowed or invested)
i = rate of interest for a single period
n = number of periods (years, or portions of a year, that the principal is outstanding)
On March 1, Ace Corporation borrowed $10,000 from a bank by signing a 4-month note with a 6% annual
simple interest rate.
How much interest will Ace Corporation owe at maturity?
- Interest = 10,000 x 6% x (4/12) = 200
What is the total amount Ace Corporation must repay at the end of the note?
- Principal plus interest = 10,000 + 200 = 10,200
Q. What is compound interest?
- Compound interest is when interest is calculated both on the initial principal but also on accumulated
interest that has not been paid or withdrawn.
Q. What does the term “periods” mean, as it relates to compound interest?
- "Periods" refers to the specific intervals at which interest is calculated and added to the principal
balance.
Q. What is the formula for Number of Periods?
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑒𝑟𝑖𝑜𝑑𝑠 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑌𝑒𝑎𝑟𝑠 × 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑𝑠/𝑌𝑒𝑎𝑟
Q. When interest is compounded more than once a year, e.g. semiannually/quarterly/monthly, why is the
interest rate divided?
- The interest rate is divided because you're breaking the year into smaller periods — and to apply
interest correctly each time, you need to use a smaller rate that corresponds to each period.
Q. What is the formula for Compounding Period Interest Rate?
𝐴𝑛𝑛𝑢𝑎𝑙 𝑅𝑎𝑡𝑒
𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑅𝑎𝑡𝑒 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐶𝑜𝑚𝑝𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑃𝑒𝑟𝑖𝑜𝑑𝑠/𝑌𝑒𝑎𝑟
Example: If you have 6% compounded annually for 5 years, then i = 6% and n = 5. If you have 6% compounded
semiannually for 5 years, then i = 3% and n = 10.
, 3
Q. What is the formula for future value of a single sum?
𝐹𝑉 = 𝑃𝑉(𝐹𝑉𝐹𝑛,𝑖 )
FV = Future value
PV = Present value
FVFn,i = Future value factor for n periods at i interest
Q. What is the formula for future value factor?
𝑛
𝐹𝑉𝐹𝑛,𝑖 = (1 + 𝑖)
FVFn,i = Future value factor for n periods at i interest
i = rate of interest for a single period
n = number of periods
𝑛
Another variation of the future value formula: 𝐹𝑉 = 𝑃𝑉(1 + 𝑖)
Put it into Practice, LO 5.1 Compute Simple and Compound Interest
Katie Boylen invests $20,000 at 6% annual interest, leaving the money invested without withdrawing any of
the interest for 6 years. At the end of the 6 years, Katie withdraws the accumulated amount of money.
a) Compute the amount Katie would withdraw assuming the investment earns simple interest.
Interest = $20,000 * 0.06 * 6 = $7,200
Amount withdrawn = $20,000 + $7,200 = $27,200
b) Compute the amount Katie would withdraw assuming the investment earns interest compounded
annually.
Here, n = 6
FV = $20,000(1 + 0.06)6 = $28,370
c) Compute the amount Katie would withdraw assuming the investment earns interest compounded
semiannually.
Here, n = 6 x 2 and i = 6 ÷ 2 = 3
FV = $20,000(1 + 0.03)12 = $28,515
5.2 Single-Sum Problems
Q. What are the 2 categories of single-sum problems?
1) Computing the unknown future value of a known single sum of money that is invested now for a
certain number of periods at a certain interest rate.
2) Computing the unknown present value of a known single sum of money in the future that is
discounted for a certain number of periods at a certain interest rate.
Q. What is the formula for the present value of a single sum?
1
𝑃𝑉 = 𝐹𝑉(𝑃𝑉𝐹𝑛,𝑖 ) 𝑜𝑟 𝑃𝑉 = 𝐹𝑉( 𝑛 )
(1+𝑖)
PV = Present value (principal or sum)
FV = Future value
PVFn,i = Present value factor for n periods at i interest
, 4
Q. What is the formula for the present value factor?
1
𝑃𝑉𝐹𝑛,𝑖 = 𝑛
(1+𝑖)
Put it into Practice, LO 5.2 Compute Future and Present Values of 1
Using the appropriate interest table, answer the question in each scenario. (Each case is independent of the
others.)
a. What is the future value of $7,000 at the end of 5 years at 8% interest compounded annually?
According to the interest table, the future value factor for n = 5, i = 8%:
FV = 7,000 * 1.46933 = $10,285
b. What is the present value of $7,000 due 8 periods from now, discounted at 6%?
According to the interest table, the present value factor for n = 8, i = 6%:
PV = 7,000 * 0.62741 = $4,392
c. Vince needs to accumulate $1,000,000 for future expansion plans. The company’s money market fund
has a balance of $92,296 and has a guaranteed interest rate of 10%. How many years (with annual
compounding) must Vince leave that balance in the fund to get his desired $1,000,000?
FV = 1,000,000 and PV = 92,296
We need to find the future value factor, knowing that i = 10%
1,000,000 ÷ 92,296 = 10.83470
10.83471 corresponds to n = 25 years
d. Assume that Vince desires to accumulate $1 million in 15 years using the money market fund balance of
$182,696. At what interest rate must Vince’s investment compound annually?
FV = 1,000,000 and PV = 182,696
We need to find the future value factor, knowing that n = 15
1,000,000 ÷ 182,696 = 5.47357
5.47357 corresponds to i = 12%
5.3 Future Value Annuities
Q. What are annuities?
- Annuities are a series of equal payments or receipts that occur at regular intervals over a specified
period.
Q. What are examples of annuities?
- Liabilities: bond interest payments, lease payments, regular pension contributions
- Assets: regular receipt of loan repayments from customers, rental income from owned properties
Q. What are the 3 requirements of annuities?
1) Periodic payments or receipts (called rents) of the same amount
2) Same-length interval between such rents
3) Compounding of interest once each interval
Q. What are the 2 types of annuities?
1) Ordinary Annuity: Rents occur at the end of each period.
2) Annuity Due: Rents occur at the beginning of each period.
